Devil May Cry 3 SE kodai:

Successfully complete the game as Dante or Vergil under the hard difficulty
setting.

Super Dante:

Successfully complete the game under the Dante Must Die difficulty setting to unlock Super Dante as a character. He has an unlimited Devil Trigger.

Vergil story mode:

Successfully complete the game under any difficulty setting.

Easy difficulty:

Intentionally fail a mission under the normal difficulty setting three to five times. A message will appear, stating that you have unlocked the easy difficulty level.

Mundus reference:

Complete the game and get the Vergil ending, where he falls down in the pool of blood. There will be three round and red electric orbs that he says he could defeat if his father did it.
This is most likely Mundus, the last Boss from the first game, because Vergil obviously loses and succumbs to Mundus' power.